Solving Fractional Partial Differential Equation By Using Wavelet Operational Method

Abstract

In this paper, we use a method based on the operational matrices to the solution of the fractional partial differential equations. The main approach is based on the operational matrices of the Haar wavelets to obtain the algebraic equations. The fractional derivatives are described in Caputo sense. Some examples are included to demonstrate the validity and applicability of the techniques.

Adomian Decomposition Method For Solving Fractional Bratu-type Equations

“…Therefore several methods for the approximate solutions to classical differential equations [11] are extended to solve differential equations of fractional order numerically. These methods include, Adomian decomposition method [12], homotopy perturbation method [13][14][15][16], homotopy analysis method [17], variational iteration method [18], generalized differential transform method [19], finite difference method [20] and etc [21,22].…”

A Numerical Method For Space Fractional Diffusion Equations Using A Semi-disrete Scheme And Chebyshev Collocation Method

“…r r (13) where the matrix elements of A are: Table 2 the maximum absolute errors for ...,0. is less than one therefore the proposed method has unique solution and is unconditionally stable [17]. Table 3 we compared our results with results of obtained in [6,15].…”

“…In [3] Darzi and et al used Sumudu transform method for solving fractional differential equations and fractional Diffusion-Wave equation. Also Neamaty [13] solved Fractional Partial Differential Equation by Using Wavelet Operational Method.…”

Solving Equal-width Wave-burgers Equation By (gg)-expansion Method

“…The EW-Burger equation is an important mathematical model arising in many different physical contexts to describe many phenomena which are simultaneously involved in nonlinearity, dissipation, dispersion, and instability, especially at the description of turbulence processes [1]. Recently, several direct methods such as Exp-function method [2,3], sine-cosine method [4,5], tanh-coth method [6], the homogeneous balance method [7], varitional iteration method and Adomian decomposition method [8], wavelet operational method [9], F-expansion method [10,11] and others have been proposed to obtain exact solutions of nonlinear partial differential equations. Using these methods many exact solutions, including the solitary wave solutions, shock wave solutions and periodic wave solutions are obtained for some kinds of nonlinear evolution equations.…”